Can I use Blender Game Engine (BGE) to create a simple interative movie?
I suggest to split the animation(s) into several segments. That means you have one ActionActuator for each segment defining the begin and end of the action to be played. E.g. start:1, end:200

To deal with each single segment I recommend to use a state of the build-in state machine. This allows to focus on the specific segment without creating too much spaghetti bricks.

Here is an example with two states. You can configure your ActionActuators as you like, but I recommend Mode:play

State A: 


State B:


As you hopefully see the structure of each state is pretty similar. 


when entering the state -> start playing 
when the playing ends ->
transit to the next state (can even be the same one, if you want to
implement a loop.


And yes, you can transit to other states on any event you like, e.g. key press.

To get more details have a look at Action sequences with logic bricks - the power of the ActuatorSensor. It comes with an example.

I hope it helps